The 86-year-old former general was hospitalized three days after he was sentenced to 80 years in prison and jailed for the massacre of indigenous people during his 1982-1983 regime.
"I have a patient who is almost 87 years old who has had a lot of stress in the last few days and weeks, and so his health has deteriorated," Carlos Alvarez, a doctor at the hospital, told reporters.
Alvarez said Rios Montt had a "high blood pressure crisis" that affected his stomach and kidneys. He could remain hospitalized for three to seven days and undergo a battery of tests, he added.
Later at the court hearing, Judge Jazmin Barrios ruled that the Guatemalan state must apologize to the Ixil Maya "for the acts of genocide" committed under Rios Montt.
She also ordered that the government declare March 23 as the National Day Against Genocide, marking the day Rios Montt took power in 1982.
The former dictator's lawyer, Francisco Garcia, said Rios Montt began to suffer from unusually high blood pressure after he was jailed at the Matamoros military facility late Friday.
Garcia said Rios Montt had not been allowed to take his medication with him when he was jailed, causing his blood pressure to rise. The former strongman has also suffered from prostate problems, he added.
Doctors examined Rios Montt at the Matamoros military facility over the weekend and recommended that he be transferred to a hospital for immediate care, the lawyer said.
His transfer was authorized by a judge but Rios Montt decided to wait until after Monday's court hearing, he said.
Rios Montt was found guilty of being behind the massacre of 1,771 Ixil Maya in the northwestern Quiche department during his dictatorship.
It was one of the bloodiest chapters of Guatemala's civil war, which lasted from 1960 to 1996 and left around 200,000 people dead or missing.